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not that simple, or that easy to think about this stuff intuitively (unless you're einstein apparently). in physics dimensions aren't thought of as strictly measuring width etc; instead the space they describe is treated as a coordinate grid, and in special relativity time is essentially one coordinate on a 4 dimensional grid. in SR time is intimately tied to space in a way temperature (or whatever else you mentioned) is not, and the fact that we can directly measure time dilation with motion is evidence SR is at least an approximation of reality.
11 would have been referring to M theory (a variation/combination of string theories) which is based in 10 spatial + 1 time dimensions. you'd be right to note that it's entirely speculative at this point, though.
I think it is intuitive.
I'll meet you for a beer at Joe's Bar at 8PM Tuesday.
That's 3 x,y,z type coordinates (Joe's Bar) and a time (8PM Tuesday).
In 3 dimensions you have freedom of movement. In the time dimension, it only moves forward. And that's the problem with it.
On the other hand, you get an infinite number of euclidian systems, which is exactly what Minkowski Space describes.
I realize that time is tied to space(time).
But it still makes as much sense to consider temperature a 4th dimension. I was rather careful in choosing temperature - Charles' Law states that the volume (x,y,z!) of a gas increases with temperature. In any case, time/temperature/whatever is not a spatial dimension.
As to the 4th dimension and bending space:
This kind of picture is used to illustrate the concept. Granted, the dent in space made by the planet or star in the picture is of all 3 dimensions, but here you see the dent is perpendicular to the 2 dimensions of the grid.
